Polar Area Moment of Inertia, Polar Section Modulus Properties of Common Shapes

The polar moment of inertia, J,
of a cross-section with respect to a polar axis, that is, an axis at right angles to the plane of
the cross-section, is defined as the moment of inertia of the cross-section with respect to the
point of intersection of the axis and the plane. The polar moment of inertia may be found by
taking the sum of the moments of inertia about two perpendicular axes lying in the plane of
the cross-section and passing through this point.

The polar section modulus (also called section modulus of torsion), Zp, for circular sections
may be found by dividing the polar moment of inertia, J, by the distance c from the
center of gravity to the most remote fiber. This method may be used to find the approximate
value of the polar section modulus of sections that are nearly round. For other than
circular cross-sections, however, the polar section modulus does not equal the polar
moment of inertia divided by the distance c.